[Footnote 17: This beautiful law is usually thus expressed: _The index of refraction of any substance is the tangent of its polarizing angle_. With the aid of this law and an apparatus similar to that figured at page 15, we can readily determine the index of refraction of any liquid. The refracted and reflected beams being visible, they can readily be caused to inclose a right angle. The polarizing angle of the liquid may be thus found with the sharpest precision. It is then only necessary to seek out its natural tangent to obtain the index of refraction.] [Footnote 18: Whewell.] [Footnote 19: Removed from us since these words were written.] [Footnote 20: The only essay known to me on the Undulatory Theory, from the pen of an American writer, is an excellent one by President Barnard, published in the Smithsonian Report for 1862.] [Footnote 21: _Boyle's Works_, Birch's edition, vol. i. pp, 729 and 730.] [Footnote 22: _Werke_, B. xxix. p. 24.] [Footnote 23: Defined in Lecture I.] [Footnote 24: This circumstance ought not to be lost sight of in the examination of compound spectra. Other similar instances might be cited.] [Footnote 25: The dark band produced when the sodium is placed within the lamp was observed on the same occasion. Then was also observed for the first time the magnificent blue band of lithium which the Bunsen's flame fails to bring out.] [Footnote 26: New York: for more than a decade no such weather had been experienced. The snow was so deep that the ordinary means of locomotion were for a time suspended.] [Footnote 27: 'Il faut reconnaître que parmi les peuples civilisés de nos jours il en est pen chez qui les hautes sciences aient fait moins de progrès qu'aux États-Unis, ou qui aient fourni moins de grands artistes, de poëtes illustres et de célèbres écrivains.' (_De la Démocratie en Amérique_, etc. tome ii. p. 36.)] [Footnote 28: At these points the two rectangular vibrations into which the original polarized ray is resolved by the plates of gypsum, act upon each other like the two rectangular impulses imparted to our pendulum in Lecture IV., one being given when the pendulum is at the limit of its swing. Vibration is thus converted into rotation.] [Footnote 29: The millimeter is about 1/25th of an inch.] INDEX. Absorption, principles of, 199 Airy, Sir George, severity and conclusiveness of his proofs, 209 Alhazen, his inquiry respecting light, 14, 207 Analyzer, polarizer and, 127 ----recompounding of the two systems of waves by the analyzer, 129 Ångström, his paper on spectrum analysis, 202 Arago, François, and Dr. Young, 50 ----his discoveries respecting light, 208 Atomic polarity, 93-96 Bacon, Roger, his inquiry respecting light, 14, 207 Bartholinus, Erasmus, on Iceland spar, 112 Bérard on polarization of heat, 180 Blackness, meaning of, 32 Boyle, Robert, his observations on colours, 65, 66 ----his remarks on fluorescence, 163, 164 Bradley, James, discovers the aberration of light, 21, 22